The distance between the two BBM leaders - Berestycki, J; Brunet, E; Graham, C; Mytnik, L; Roquejoffre, J-M; Ryzhik, L (IOP Publishing, 2022)
We study the distance between the two rightmost particles in branching Brownian motion. Derrida and the second author have shown that the long-time limit d 12 of this random variable can be expressed in terms of PDEs related to the Fisher-KPP equation. We use such a representation to determine the sharp asymptotics of a)$?> P(d12>a) as a → +∞. These tail asymptotics were previously known to 'exponential order;' we discover an algebraic correction to this behavior.